| 方向导数与二元函数极值的充分条件 |
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| 引用本文： | 杨金花,田冲. 方向导数与二元函数极值的充分条件[J]. 平顶山学院学报, 2011, 26(5): 11-14,20 |
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| 作者姓名： | 杨金花 田冲 |
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| 作者单位： | 1. 河南理工大学,河南焦作,454000
2. 周口师范学院,河南周口,466000 |
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| 摘 要： | 分别给出了P0(x0,y0)的l0珒正方向δ邻域和l0珒负方向δ邻域的定义,用方向导数表示了二元函数的泰勒公式,使之与一元函数的泰勒公式有统一的形式;并利用二元函数泰勒公式的方向导数形式给出了二元函数取得极值的3个充分条件,使之与一元函数取得极值的3个充分条件相对应.
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| 关 键 词： | 方向导数 极值 二元函数 泰勒公式 |
Directional Derivative and the Sufficient Condition of the Extreme Value for Two-variable Function |
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| YANG Jin-hua,TIAN Chong. Directional Derivative and the Sufficient Condition of the Extreme Value for Two-variable Function[J]. Journal of Pingdingshan University, 2011, 26(5): 11-14,20 |
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| Authors: | YANG Jin-hua TIAN Chong |
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| Affiliation: | YANG Jin-hua1,TIAN Chong2(1.Henan Polytechnic University,Jiaozuo,Henan 454000,China,2.Zhoukou Normal University,Zhoukou,Henan 466000,China) |
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| Abstract: | In this paper,the definition of positive direction neighborhood of a point P0(x0,y0) and its negative direction neighborhood are given.Taylor's formula of two-variable function is given by the use of directional derivative,which is in accord with Taylor's formula of one-variable function.Meanwhile,three sufficient conditions of two-variable function extreme value are given with directional derivative of Taylor's formula of two-variable function,which are in accord with one-variable function. |
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| Keywords: | directional derivative extreme value two-variable function Taylor's formula |
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